Relevant bibliographies by topics / Cutting stock problem Mathematical models

Academic literature on the topic 'Cutting stock problem Mathematical models'

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Published: 10 December 2022
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Journal articles on the topic "Cutting stock problem Mathematical models"

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Poltroniere, Sônia Cristina, Silvio Alexandre Araujo, and Kelly Cristina Poldi. "Optimization of an Integrated Lot Sizing and Cutting Stock Problem in the Paper Industry." TEMA (São Carlos) 17, no. 3 (December 20, 2016): 305. http://dx.doi.org/10.5540/tema.2016.017.03.0305.

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Two important optimization problems occur in the planning and production scheduling in paper industries: the lot sizing problem and the cutting stock problem. The lot sizing problem must determine the quantity of jumbos of different types of paper to be produced in each machine over a finite planning horizon.These jumbos are then cut in order to meet the demand of items for each period. In this paper, we deal with the integration of these two problems, aiming to minimize costs of production and in- ventory of jumbos, as well as the trim loss of paper generated during the cutting process. Two mathematical models for the integrated problem are considered, and these models are solved both heuristically and using an optimization package. Attempting to get lower bounds for the problem, relaxed versions of the models also have been solved. Finally, computational experiments are presented and discussed.
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Farley, Alan A. "Mathematical Programming Models for Cutting-Stock Problems in the Clothing Industry." Journal of the Operational Research Society 39, no. 1 (January 1988): 41. http://dx.doi.org/10.2307/2581997.

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Farley, Alan A. "Mathematical Programming Models for Cutting-Stock Problems in the Clothing Industry." Journal of the Operational Research Society 39, no. 1 (January 1988): 41–53. http://dx.doi.org/10.1057/jors.1988.6.

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Delorme, Maxence, Manuel Iori, and Silvano Martello. "Bin packing and cutting stock problems: Mathematical models and exact algorithms." European Journal of Operational Research 255, no. 1 (November 2016): 1–20. http://dx.doi.org/10.1016/j.ejor.2016.04.030.

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Poldi, Kelly Cristina, and Silvio Alexandre de Araujo. "Mathematical models and a heuristic method for the multiperiod one-dimensional cutting stock problem." Annals of Operations Research 238, no. 1-2 (January 18, 2016): 497–520. http://dx.doi.org/10.1007/s10479-015-2103-2.

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Wang, Fu-Kwun, and Feng-Tai Liu. "Flexible Stock Allocation and Trim Loss Control for Cutting Problem in the Industrial-Use Paper Production." Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/521386.

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We consider a one-dimensional cutting stock problem (CSP) in which the stock widths are not used to fulfill the order but kept for use in the future for the industrial-use paper production. We present a new model based on the flexible stock allocation and trim loss control to determine the production quantity. We evaluate our approach using a real data and show that we are able to solve industrial-size problems, while also addressing common cutting considerations such as aggregation of orders, multiple stock widths, and cutting different patterns on the same machine. In addition, we compare our model with others, including trim loss minimization problem (TLMP) and cutting stock problem (CSP). The results show that the proposed model outperforms the other two models regarding total flexibility and trim loss ratio.
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Sá Santos, José Victor, and Napoleão Nepomuceno. "Computational Performance Evaluation of Column Generation and Generate-and-Solve Techniques for the One-Dimensional Cutting Stock Problem." Algorithms 15, no. 11 (October 25, 2022): 394. http://dx.doi.org/10.3390/a15110394.

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The Cutting Stock Problem (CSP) is an optimisation problem that roughly consists of cutting large objects in order to produce small items. The computational effort for solving this problem is largely affected by the number of cutting patterns. In this article, in order to cope with large instances of the One-Dimensional Cutting Stock Problem (1D-CSP), we resort to a pattern generating procedure and propose a strategy to restrict the number of patterns generated. Integer Linear Programming (ILP) models, an implementation of the Column Generation (CG) technique, and an application of the Generate-and-Solve (G&S) framework were used to obtain solutions for benchmark instances from the literature. The exact method was capable of solving small and medium sized instances of the problem. For large sized instances, the exact method was not applicable, while the effectiveness of the other methods depended on the characteristics of the instances. In general, the G&S method presented successful results, obtaining quasi-optimal solutions for the majority of the instances, by employing the strategy of artificially reducing the number of cutting patterns and by exploiting them in a heuristic framework.
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Li, Yan Cang, Juan Juan Suo, and Shu Jing Zhou. "Improved ACO for Dimensional Cutting-Stock Problem." Applied Mechanics and Materials 26-28 (June 2010): 277–80. http://dx.doi.org/10.4028/www.scientific.net/amm.26-28.277.

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In order to find an effective method for solving the NP problem-dimensional cutting stock problem, the improved ACO based on entropy was introduced．After introducing the basic knowledge of the improved ACO, the dimensional cutting-stock problem’s mathematical model was set up．And the improved ACO was employed to optimize the problem．Computed results indicate that the ant colony algorithm can approach the theoretical optimal solution，and its astringency is good．This study provides a new approach for the optimization of the NP hard problems.
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Arenales, Marcos Nereu, Adriana Cristina Cherri, Douglas N. do Nascimento, and Andréa Vianna. "A NEW MATHEMATICAL MODEL FOR THE CUTTING STOCK/LEFTOVER PROBLEM." Pesquisa Operacional 35, no. 3 (December 2015): 509–22. http://dx.doi.org/10.1590/0101-7438.2015.035.03.0509.

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Sugi, Masao, Yusuke Shiomi, Tsuyoshi Okubo, Kazuyoshi Inoue, and Jun Ota. "A Solution for 2D Rectangular Cutting Stock Problems with 3-Stage Guillotine-Cutting Constraint." International Journal of Automation Technology 4, no. 5 (September 5, 2010): 461–68. http://dx.doi.org/10.20965/ijat.2010.p0461.

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The cutting stock problem (CSP) adversely affecting processing industry profits has been studied aggressively in mathematical planning but the results are not often used at real production sites and solutions are often still found manually by experienced personnel because real processing constraints have not been focused on. This paper deals with the 2-dimensional rectangular cutting stock problem (2DRCSP) in which the shape of a cut piece is rectangular, assuming a roll-shaped stock often used in actual processing and proposing a solution taking processing called 3-stage guillotine cutting into account.
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Dissertations / Theses on the topic "Cutting stock problem Mathematical models"

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Wong, Chun Chuen. "Graph approach modeling and optimal heuristics for the one-dimensional cutting and packing problems." HKBU Institutional Repository, 2002. http://repository.hkbu.edu.hk/etd_ra/444.

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Hallbäck, Sofia, and Ellen Paulsson. "Reducing waste with an optimized trimming model in production planning." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-173253.

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In which ways can the process of trimming dispersion coated board products be optimized so as to reduce material waste and increase production efficiency? This is the question that this master thesis report seeks to answer. In paper production, alot of waste is generated when cutting production reels into customer reels. Some material waste are necessary in order to ensure good quality, however a large amount of the wastecould be reduced if the cutting process was to be optimized. During this project, carried out at a forest company, a mathematical optimization model was developed in order to reduce waste and save costs. This model is based on a cutting stock problem using column generation approach. It provides as its output cutting patterns and an optimal allocation of rolls for production purposes, which implies minimizing the number production rolls needed.The visualization of the results could also be used to achieve optimal stock levels, and easier keep track on how to use the material available in stock. Findings show that there are potential savings to be done. Simulations suggest an implementation of this model could result in material savings of around 7 %. This could also translateto environmental savings in CO2, where every decrease of one tonne material equals to adecrease in CO2emissions of 500 kg
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Marciniuk, Fernanda Ledo. "Uma aplicação do algoritmo colonia de formigas no problema de corte ordenado." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306264.

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Orientadores: Antonio Carlos Moretti, Luis Leduino de Salles Neto
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: O problema de corte de estoque ordenado, um problema relativamente novo na literatura, e uma adaptação do problema de corte de estoque tradicional onde algumas restrições quanto a limitação do numero de ordens de produção em processamento são adicionadas. Esta dissertação tem como objetivo estudar uma nova abordagem deste problema utilizando uma aplicação da metaheurística colônia de formigas. Esta metaheurística utiliza os princípios de auto-organização de uma população de formigas visando a resolução de problemas de otimização combinatorial
Abstract: The Ordered Cutting Stock Problem (OCSP), a relatively recent problem in technical literarture, is a variant of the more well-known Cutting Stock Problem (CSP). This variant includes some new constraints in the mathematical formulation, regarding the number of production orders being processed simultaneously. This work studies a new approach to solve the OCSP, applying the Ant Colony Optimization (ACO) metaheurisitic. This metaheuristic is based in the self-organizing principles that govern ant population's behaviour, solving combinatorial optimization problems
Mestrado
Pesquisa Operacional
Mestre em Matemática Aplicada
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Coutinho, Maiko Willian. "O problema de corte de estoque e aplicações /." São José do Rio Preto, 2019. http://hdl.handle.net/11449/191339.

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Orientador: Sônia Cristina Poltroniere Silva
Resumo: A Matemática está constantemente presente em nosso cotidiano, sendo ferramenta importante para uma melhor compreensão do mundo e facilitadora dos processos de tomada de decisão. Neste sentido, o trabalho com resolução de problemas ao longo da formação escolar básica faz-se extremamente necessário. Inserida neste contexto, a modelagem matemática é uma ferramenta que permite uma melhor leitura e um tratamento mais adequado do problema. Essa dissertação aborda, inicialmente, conceitos básicos relativos ao Problema de Corte de Estoque e a sua modelagem matemática, com ênfase na definição dos padrões de corte. Posteriormente, é discutido o método branch-and-bound, utilizado na resolução de problemas de otimização linear inteira, como é o caso do problema de corte. Por m, são propostas duas situações-problema, que consideram aplicações do Problema de Corte, para serem trabalhados com alunos do Ensino Médio, considerando os conceitos matemáticos assimilados previamente.
Abstract: Mathematics is constantly present in our daily lives, being an important tool for a bet ter understanding of the world and facilitating decision making processes. In this sense, problem-solving work throughout basic school education is extremely necessary. In this context, mathematical modeling is a tool that allows a better reading and a better treat ment of the problem. This dissertation initially addresses the basic concepts related to the Cutting Stock Problem and the mathematical modeling for the one-dimensional case, with emphasis on the de nition of the cutting patterns. Subsequently, the Branch-and-bound method, used in solving Integer Linear Programming Problems, such as the cutting pro blem, is discussed. Finally, problem situations are proposed, which consider applications of the Cutting Stock Problem, to be worked with high school students, emphasizing the previously assimilated mathematical concepts.
Mestre
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Ravelo, Santiago Valdes. "Modelos matemáticos e algoritmos para problemas combinatórios." Universidade Federal de Goiás, 2011. http://repositorio.bc.ufg.br/tede/handle/tede/5354.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This work considers three relevant NP-hard problems. The firstone is the one-dimensional cutting stock problem in which the non-used material in the cutting patterns may be used in the future. For this problem we analyze the existing mathematical models, propose new models, design a heuristic and two metaheuristic approaches, being their performances improved by using parallel programming, and solve instances, practical and randomly generated, from the literature. The computational experiments were quite good for all tested instances. The second problem we consider is the stable roommates problem (a variant of the stable matching problem). For this we give two mathematical programming models, sequential and parallel implementations of a Tabu Search, and a Branch-andBound. Also, we report computational experiments to instances of the problem. The last problem we consider is the compartmentalized knapsack problem (a generalization of the knapsack problem) for which we analyze a quadratic integer model and give a linear integer model. We design a greedy heuristic and a GRASP algorithm, that uses path-relinking, and solve randomly generated instances. All parallel implementations use Graphics Processing Units (GPUs).
Este trabalho considera três problemas, NP-difíceis, relevantes de estudo em otimização combinatória. O primeiro deles é o problema de corte uni-dimensional de objetos, onde o material não usado pelos padrões de corte pode ser usado no futuro. Para este problema analisamos os modelos matemáticos existentes, propomos novos modelos, projetamos uma heurística construtiva e duas metaheurísticas, sendo seus desempenhos melhorados com programação paralela, e resolvemos instâncias, práticas e aleatórias, encontradas na literatura; sendo os experimentos computacionais muito bons para todas as intânciastestadas.Osegundoproblemaqueconsideramoséoproblemadoscompanheiros estáveis (stable roommates problem), uma variante do problema de emparelhamento estável (stable matching problem). Para este propomos dois modelos matemáticos, uma implementação sequencial e uma paralela de uma Tabu Search, e um Branch-andBound. Também reportamos experimentos computacionais para instâncias do problema. O último problema considerado é o da mochila compartimentada (uma generalização do problema clássico da mochila), para o qual analisamos uma modelagem quadrática inteira e propomos um modelo linear inteiro; também projetamos uma heurística gulosa, um algoritmo GRASP, que usa path-relinking, e resolvemos intâncias geradas aleatóriamente. Todas as implementações em paralelo usam unidades de processamento gráfico (Graphics Processing Units, GPUs).
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Yu-ChingLiu and 劉育青. "Using Mathematical Programming and Heuristic Methods to Solve the Cutting Stock Problem for Bias Product." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/15669696690420369037.

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碩士
國立成功大學
工業與資訊管理學系專班
98
The cutting stock problem (CSP) was classified to NP-Hard problem. Most scholars used the mathematical with heuristic methods to solve rectangle space cutting problem. In TFT-LCD industrial, some high polymer film need be used with angle in inlayer. To achieve the customer request, the material need be cut with angle and that will cause some useless triangle part. We not found any paper discuss about the bias product cutting problem as our searching. This paper will use mathematical with heuristic methods to solve bias product cutting problem. We will show the mathematical model of the bias product cutting process by guillotine, before to construct mathematical programming model. After the mathematical model constructed, the basic yield and basic pattern will defined. In order to get higher yield, we try to use four kinds of heuristic methods to fill the available product in useless space and to verify the best one. In this paper, we used real order data that got from a polarizer maker to verify our model. We suggested using Best Fit (BF) heuristic methods to solve the problem and approved our methods could help to get more usage part than the original polarizer maker. By the research result, also suggest controlling material width、material width quantity and calculating volume of orders to get more benefit.
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Books on the topic "Cutting stock problem Mathematical models"

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Archibald, T. W. An optimal policy for a two depot inventory problem with stock transfer. Edinburgh: University of Edinburgh, Management School, 1994.

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Instituti i Informatikës dhe Matematikës së Aplikuar (Akademia e Shkencave e RSH), ed. Përmbledhje punimesh në informatikë dhe matematikë të aplikuar. Tiranë: Republika e Shqipërisë Akademia e Shkencave, Instituti i Informatikës dhe Matematikës së Aplikuar, 1995.

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Book chapters on the topic "Cutting stock problem Mathematical models"

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Nickels, W. "A Knowledge-Based System for Integrated Solving Cutting Stock Problems and Production Control in the Paper Industry." In Mathematical Models for Decision Support, 471–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-83555-1_28.

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Ripatti, Artem V., and Vadim M. Kartak. "Sensitive Instances of the Cutting Stock Problem." In Mathematical Optimization Theory and Operations Research, 80–87. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-58657-7_9.

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Ripatti, Artem V., and Vadim M. Kartak. "Bounds for Non-IRUP Instances of Cutting Stock Problem with Minimal Capacity." In Mathematical Optimization Theory and Operations Research, 79–85. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-33394-2_7.

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Qu, Shengyuan, Zhongwen Luo, Zhen Wang, and Hongzhou Wang. "Forest Benefit-Rotation Model Considering Carbon Sequestration, Ecological and Social Benefits." In Advances in Transdisciplinary Engineering. IOS Press, 2022. http://dx.doi.org/10.3233/atde220298.

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Forest ecosystems are the largest terrestrial carbon sink, making important contributions to atmospheric regulation, stability of the biosphere and eco nomic benefits to society. In order to manage forests properly, this paper makes forest management recommendations, including logging through mathematical modeling. Firstly, this paper uses the Logistic function to establish a Tree Growth model to simulate the growth of tree species. A piecewise periodic function is introduced to obtain a Tree Growth-Felling model. Secondly, combined with specific forest data including α, dominant tree species and initial age distributions, Forest Carbon Sequestration Model that assesses sequestration stock can be established. Then this paper comprehensively considers the carbon sequestration, ecological benefits and social production value of the forest, and gives a benefit assessment model. Under the modification of this model, decisions can be made on the rotation period of forests. Through the analysis, it can be found that the appropriate cycle of cutting is the best management of forest. Finally, this paper uses the above models to evaluate Lishan National Nature Reserve in Shanxi Province. When the forest benefit is the largest, the best cutting rotation is 28 years. In 100 years, 224 million yuan of benefit can be obtained and 3.103×106 tons of carbon can be fixed.
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Gönül Sezer, Eylül Damla, and Duygun Fatih Demirel. "Examining the Effects of Mucilage in the Marmara Sea on Fisheries, Tourism, and Maritime Transportation via the System Dynamics Approach." In Handbook of Research on Water Sciences and Society, 101–22. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-7998-7356-3.ch005.

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The Marmara Sea, which is of great importance for Turkey, has been facing a serious mucilage problem since the last quarter of 2020 due to various natural and human-induced factors. In addition to the negative effects of the observed mucilage explosion on the marine ecosystem and human health, studies in the literature emphasize the inevitability of critical negative economic consequences of mucilage, especially on the fishing, tourism, and maritime transport sectors. However, there is no study in the literature to analyze the effects of policies aimed at eliminating mucilage or preventing its re-emergence with a mathematical method. Therefore, in this chapter, a dynamic model is proposed to analyze the effects of the mucilage in the Marmara Sea on fisheries, tourism, and maritime transport. Here, the proposed conceptual and stock-flow models reflect the complex relationships among causes of mucilage, mucilage level, fisheries, tourism, and maritime transport sectors, and preventive actions.
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Conference papers on the topic "Cutting stock problem Mathematical models"

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Lazoglu, Ismail, and Yusuf Altintas. "Prediction of Tool and Chip Temperature in Continuous Metal Cutting and Milling." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-1895.

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Abstract A finite difference method is presented to predict tool and chip temperature fields in continuous machining and time varying milling processes. Continuous machining operations like orthogonal cutting are studied by modeling the heat transfer between the tool and chip at the contact zone. The shear energy created in the primary zone, the friction energy produced at the rake face - chip contact zone and the heat balance between the moving chip and stationary tool are considered. The temperature distribution is solved using finite difference method. Later, the model is extended to milling where the cutting is interrupted and the chip thickness varies with time. The time varying chip is digitized into small elements with differential cutter rotation angles. The temperature field in each differential element is modeled as a first order dynamic system, whose time constant is identified based on the thermal properties of the tool and work material, and the initial temperature at the previous chip segment. The transient temperature variation is evaluated by recursively solving the first order heat transfer problem at successive chip elements. The proposed model combines the steady-state temperature prediction in continuous machining with transient temperature evaluation in interrupted cutting operations where the chip and the process change in a discontinuous manner. The mathematical models and simulation results are in satisfactory agreement with experimental temperature measurements reported in the literature.
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Рязанов, С., S. Ryazanov, Михаил Решетников, and Mihail Reshetnikov. "Geometrical Model of the Manufacturing Surface of the Equivalent Working Surface of the Fine Tooth Dolbyak." In 29th International Conference on Computer Graphics, Image Processing and Computer Vision, Visualization Systems and the Virtual Environment GraphiCon'2019. Bryansk State Technical University, 2019. http://dx.doi.org/10.30987/graphicon-2019-1-196-200.

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Existing mathematical models for calculating gearing are quite complex and do not always make it possible to quickly and accurately obtain the desired result. A simpler way to find a suitable gear option that satisfies the task is to use computer modeling and computer graphics methods, and in particular solid-state modeling algorithms. The use of geometric modeling techniques to simulate the process of shaping the working surface of gearing is based on the relative movement of intersecting objects in the form of a “workpiece-tool” system. This allows you to obtain the necessary geometric model that accurately reproduces the geometric configuration of the surfaces of the teeth of spatial gears, taking into account the technological features of their production on gear cutting machines. This information allows you to perform on the computer imitation control the movement of the cutting tool. Ultimately, this boils down to the problem of analytic description and computer representation of curves and surfaces in three-dimensional space. As the gear cutting tools, the most widely used are disk and worm modular mills (shaver), gear cutting heads, dolbyaki and lath tools. At the moment there are no computer algorithms for obtaining the “dolbyak” producing surfaces, which are obtained by a tool with a modified producing surface. A change in the geometric shape of the tool producing surface will lead to a change in its working surfaces, which may lead to an improvement in their contact. This article shows the application of the developed methods and algorithms of geometric and computer modeling, which are intended for shaping the working surfaces of the Dolbyak tool. Their application will speed up the process of calculating intermediate adjustments of machines used for cutting gears, bypassing complex mathematical calculations that, under conditions of aging of the gear-cutting machines, their wear and the inevitable reduction in the accuracy of their kinematic chains.
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Berezkin, Vladimir, Anar Sharifov, Elena Khatmullina, Evgeniy Yudin, and Ildus Khatmullin. "A Tool and Mathematical Model for Estimation of Wells Initial Water-Cut and Residual Oil Reserves on Large-Sized Oil Fields." In SPE Annual Caspian Technical Conference. SPE, 2021. http://dx.doi.org/10.2118/207076-ms.

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Abstract Oil production forecasting and well intervention planning require an accurate estimation of the remaining oil in place (ROIP). The problem of ROIP maps generation can be solved using commercial software; however, in the case of large fields, this requires significant computing resources and takes a big amount of time to prepare and adapt the data. Mathematical models for getting a quick solution to these issues have not been sufficiently elaborated. In this work a physical and mathematical model is proposed for building ROIP, oil saturation and water cut maps. The model was used to develop a tool for well stock managing, new wells drilling planning and detection of behind casing fluid flow by comparing the actual water cut of the well with the calculated water cut map.
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Berezkin, Vladimir, Anar Sharifov, Elena Khatmullina, Evgeniy Yudin, and Ildus Khatmullin. "A Tool and Mathematical Model for Estimation of Wells Initial Water-Cut and Residual Oil Reserves on Large-Sized Oil Fields." In SPE Annual Caspian Technical Conference. SPE, 2021. http://dx.doi.org/10.2118/207076-ms.

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Abstract Oil production forecasting and well intervention planning require an accurate estimation of the remaining oil in place (ROIP). The problem of ROIP maps generation can be solved using commercial software; however, in the case of large fields, this requires significant computing resources and takes a big amount of time to prepare and adapt the data. Mathematical models for getting a quick solution to these issues have not been sufficiently elaborated. In this work a physical and mathematical model is proposed for building ROIP, oil saturation and water cut maps. The model was used to develop a tool for well stock managing, new wells drilling planning and detection of behind casing fluid flow by comparing the actual water cut of the well with the calculated water cut map.
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Lortz, Wolfgang, and Radu Pavel. "Advanced Modeling of Drilling – Realistic Process Mechanics Leading to Helical Chip Formation." In ASME 2021 16th International Manufacturing Science and Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/msec2021-63790.

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Abstract There is considerable interest in the “Industry 4.0 project”. Industry hopes that a general solution of the metal removal problem will be found through the use of highly automated manufacturing data. Scientists hope that the computer will provide better models based on artificial intelligence and machine learning. Initial attempts leveraging existing models did not result in satisfactory results yet — largely because of mathematical, physical and metallurgical reasons. This paper presents a new mathematical-physical model to describe the total process mechanics from volume conservation, to friction, to metal plasticity with self-hardening or softening effects and dynamic phenomena during metal plastic flow. The softening effects are created by high energy corresponding to high strain-rate resulting in high temperatures. Furthermore, the developed equations for strain-rate discontinuities as well as yield shear stress with body forces have an interdependent relationship and lead to plastic deformation with dynamic behavior in the total chip formation zone. This plastic deformation is the only parameter that will not disappear after completing the process. This leads to the opportunity to check the theoretically developed grid deformation and compare it with practical results of the same area. In this publication this new theory will be used to analyze the complex contact and friction conditions between the chip and tool edge of a twist drill during operation. It will be shown that the existing conditions are leading to high wear at the corner edge and flank wear at the tool cutting edge. In addition, the existing temperatures can be estimated and compared with practical measurements, and all these complex and difficult conditions create a helical spiral chip, which could be developed as it will be presented in this paper.
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